Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×Dic17 | C2 | semidirect |
| 3. #11763145 | C2 | semidirect |
| 5. #11763118 | C2 | semidirect |
| 6. #11763029 | C2 | semidirect |
| 7. #11762965 | C2 | semidirect |
| 8. #11762913 | C2 | semidirect |
| 9. #11762910 | C2 | semidirect |
| 10. #11762863 | C2 | semidirect |
| 174. C17 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763340 | 2 |
| C2×Q8×Dic17 | 2 |
| #11763145 | 2 |
| #11763125 | 2 |
| #11763118 | 2 |
| #11763029 | 2 |
| #11762965 | 2 |
| #11762913 | 2 |
| #11762910 | 2 |
| #11762863 | 2 |
| C17×#448 | 2 |
| #3117 | 17 |